1 PESO
worn: $100
average circulated: $200
well preserved: $300
fully uncirculated: $600
These values apply to all dates, 1881, 1882, and 1883.
The 1882 coin is more common in lower grades, divide the 'worn' and 'average circulated' values by two for an 1882 coin.

Be careful of counterfeits of the valuable coins.

When doing an appraisal, Burl, I usually start with the catalogs and then check the web, usually eBay, Google image searches and my old haunts dealer sites. I could not find a single genuine 1881 Argentina 10 Centavos anywhere. And I only found one Chinese fake. One of my favorite World Coin dealers is VCoins. You might check with him.